Sum of Squares

The number \(648000\) can be represented in two ways as the sum of two perfect squares, as follows:

\({ a }^{ 2 }+{ b }^{ 2 }=648000\) and \({ c }^{ 2 }+{ d }^{ 2 }=648000\), such that \(a\neq b\neq c\neq d\), and \(a, b, c, d\) are positive integers.

Find \(a+b+c+d\)

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